To perform this test, select.
For example, the manager of a pizza business collects a random sample of pizza delivery times. The manager uses the 1-sample t-test to determine whether the mean delivery time is significantly lower than a competitor's advertised delivery time of 30 minutes.
The test calculates the difference between your sample mean and the hypothesized mean relative to the variability of your sample. Usually, the larger the difference and the smaller the variability in your sample, the greater the chance that the population mean differs significantly from the hypothesized mean.
The 1-sample t-test also works well when the assumption of normality is violated, but only if the underlying distribution is symmetric, unimodal, and continuous. If the values are highly skewed, it might be appropriate to use a nonparametric procedure, such as a 1-sample sign test.
|H0: μ = µ0||The population mean (μ) equals the hypothesized mean (µ0).|
|H1: μ ≠ µ0||The population mean (μ) differs from the hypothesized mean (µ0).|
|H1: μ > µ0||The population mean (μ) is greater than the hypothesized mean (µ0).|
|H1: μ < µ0||The population mean (μ) is less than the hypothesized mean (µ0).|